JSM 2004 - Toronto

Abstract #302146

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Activity Number: 429
Type: Contributed
Date/Time: Thursday, August 12, 2004 : 10:30 AM to 12:20 PM
Sponsor: Section on Quality and Productivity
Abstract - #302146
Title: New Control Charts for the Mean of the Poisson Distribution
Author(s): John Aleong*+
Companies: University of Vermont
Address: Dept. of Mathematics and Statistics, Burlington, VT, 05495,
Keywords: Brown ; Brown/Edgeworth expansions ; simulations
Abstract:

The problem of the control charts for the mean of the Poisson distribution (c-charts) will be revisited. The c-chart is based on the standard Wald confidence interval. Brown et al. (2003) and Aleong (2003) discuss the erratic behavior of the coverage probability of the Wald confidence interval. Recent results by Brown, Cai, and DasGupta (2000, 2001, 2002, 2003), have shown theoretically, using Edgeworth expansions and simulations, the eccentric behavior of the Wald confidence interval for mean of the of the natural exponential family using a quadratic variance function. Aleong (2003) gave new control charts for the binomial proportion. Using the coverage probabilities and expected length of the intervals, Brown et al. compared the Wald confidence interval with other intervals. Equal tail Jeffrey interval and the likelihood ratio interval are better than the Wald interval, which is the basis of the c and u charts. Hence the standard control limits, which are based on the Wald interval, are unlikely to represent actual three-sigma limits. The Wald intervals are particularly prone to erratic behavior.

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